摘要
本文研究一类生化反应的微分方程 dx/dt=1-x^py^q,dy/dt=α(x^py^q-y),其中p,q∈z^+,α>0。对p=1,q≥3和p=2,q=2,我们给出一些定性结果。
In this paper, it is studied that multimolecules reactions with the differential equation dx/dt=1-xp^py^q, dy/dt=α(x^py^q-y), (*)where p, q∈z^+ and α>0. The following results are obtained: For p=1 and q≥3, there exists a constant α~*(q), 1/(q-1)<a~*(q)<2(q+1)q^1/(2q-3), suchthat the system (*) has unique stable limit cycle for 1/(q-1)<α<α~*(q),and the system (*) has no close orbit for a∈(0,1/(q-1)]∪[α~*(q), +o∞];for p=2 and q=2, the system(*)has a stable limit cycle for 0<α-2《1 and (*)has no close orbit for α∈(0,4/3^(1/3)∪(8/3^(1/2)+∞).
出处
《生物数学学报》
CSCD
北大核心
1990年第2期162-170,共9页
Journal of Biomathematics
关键词
微方程
闭轨
极限环
differential equation, close orbit, limit cycle.
